ARCH 435 PROJECT MANAGEMENT

1. ARCH 435PROJECT MANAGEMENT Lecture 3: Project Time Planning (Arrow Diagramming Technique) Activity on Arrow (AOA)

2. Each activity (task) is portrayed or presented by an arrow. The tail and head of the arrow denote the start and finish of the activity whilst its duration is shown in brackets below. The length of the arrow has no significance neither has its orientation. • ARROW DIAGRAM Activity Site Preparation ] Duration] ] 30]

3. As means of further defining the point in time, when an activity starts or finishes, start and finish events are added. An event (= node = connector), unlike an activity, does not consume time or resources, it merely represents a point in timeat which something happens. Numbers are given to the events to provide a unique identity to each activity. The first event in a project schedule is the start of the project. The last event in a project schedule is the end of the project. • ARROW DIAGRAM

4. Activity Identification Start Event Finish Event Activity 10 20 [Duration] Activity identification numbers called event numbers

5. i-j Numbers of Events j i Activity Duration • The node at the tail of an arrow is the i-node. • The node at the head of an arrow is the j-node.

6. The network (the graphical representation of a project plan) must have definite points of beginning and finish. (The accuracy and usefulness of a network is dependent mainly upon intimate knowledge of the project itself, and upon the general qualities of judgment and skill of the planning personnel.) The arrows originate at the right side of a node and terminate at the left side of a node. Any two events may be directly connected by no more than oneactivity. Use symbols to indicate crossovers to avoid misunderstanding. • Rules of Making Arrow Diagram

7. Logical Relationships 10 20 30 A B • Node “20” is the j-node for activity “A” and it is also the i-node for activity “B”. Therefore, activity “A” is a predecessor to activity “B”. • In other words activity “B” is a successor to activity “A”. • Activity B depends on activity A.

8. Logical Relationships Succeeding activities 30 10 20 40 50 • Event numbers must not be duplicated in a network. • j-node number is always greater than i-node number.

9. 80 180 120 170 190 160 • Logical Relationships Concurrent activities (happens at the same time)

10. The network must be a logical representation of all the activities. Dummy Activities are used, where necessary for: Unique numbering, and Logical sequencing. Dummy activityis an arrow that represents merely a dependency of one activity upon another. A dummy activity has a zero time. It is also called dependencyarrow. • Rules of Making Arrow Diagram

11. Dummy Activities • The following network shows incorrect activity numbering. 90 A 50 70 80 100 B 110 60

12. Dummy Activities • For unique numbering, use a dummy activity. 75 90 A 50 70 80 100 B 110 60

13. 40 10 20 50 30 • Dummy Activities For representing logical relationships, you may need dummy activities. A C B D In this diagram: Activity C depends on Activities A, B. Activity D depends on Activities A, B. LETS SAY, Activity C depends on Activity A ONLY, and Activity D depends on Activities A, B. How can we represent this relationship?

14. 50 40 10 20 30 • Dummy Activities In this case, use a dummy activity to indicate the correct relationship. C A B D 35 Now, Activity C depends on Activities A ONLY. Activity D depends on Activities A, B.

15. There must be no "looping" in the network. The loop is an indication of faulty logic. The definition of one or more of the dependency relationships is not valid. 90 100 120 130 110 • Rules of Making Arrow Diagram

16. The network must be continuous (without unconnected activities). 30 60 100 10 20 50 90 120 40 70 110 80 • Rules of Making Arrow Diagram

17. Networks should have only one initial event and only one terminal event. • Rules of Making Arrow Diagram 30 60 10 20 50 90 120 40 70 110

18. Before an activity may begin, all activities preceding it must be completed (the logical relationship between activities is (finish to start). • Rules of Making Arrow Diagram

19. Earliest Event Time Activity Activity Event Label Latest Event Time Tail Head • Network Analysis (Computation) Occurrence times of Events = Early and late timings of event occurrence = Early and late event times Standard layout for recording data

20. Early Event Time (EET = E =TE) Early Event Time (Earliest occurrence time for event) is the earliest time at which an event can occur, considering the duration of precedent activities. Forward Pass for Computing EET Each activity starts as soon as possible, i.e., as soon as all of its predecessor activities are completed. Direction: Left to right, from the beginning to the end of the project Set: EET of the initial node = 0 Add:EETj = EETi + Dij Take the maximum The estimated project duration = EET of the last node. j Activity EETj EETi i Dij

21. 0 3 4 12 10 20 30 40 A B C 1 8 3 • Early Event Times (EET = E =TE)

22. K 4 L 80 40 9 M 5 12 • Early Event Times (TE) 4 15 24 70 50

23. 40 10 30 20 50 60 70 3 2 3 4 4 5 7 3 1 • Early Event Times (TE) Example:

24. 40 10 0 3 30 20 50 60 70 3 2 3 4 4 5 7 3 1 • Early Event Times (TE) 2 8 4 16 9

25. Late Event Time (LET = L =TL) Late Event Time (Latest occurrence time of event) is the latest time at which an event can occur, if the project is to be completed on schedule. Backward Pass for Computing LET Direction: Right to left, from the end to the beginning of the project Set: LET of the last (terminal) node = EET . Subtract:LETi = LETj - Dij Take the minimum j EETi Activity EETj i LETi LETj Dij

26. 16 16 8 13 • Late Event Times (TL) 50 3 60 9 7 40 9

27. 2 10 4 0 3 30 50 60 70 20 3 2 3 4 4 5 7 3 1 • Late Event Times (TL), Example: 8 16 9 40

28. 2 10 4 40 0 3 20 30 50 60 70 3 2 3 4 4 5 7 3 1 • Late Event Times (TL), Example: 8 10 13 16 16 4 0 9 9 8

29. Network Analysis (Computation) Activity Times (Schedule) Early Start (ES): The earliest time at which an activity can be started. ESij = EETi Early Finish (EF): The earliest time at which an activity can be completed. EFij = ESij + Dij Late Finish (LF): The latest time at which an activity can be completed without delaying project completion. LFij = LETj Late Start (LS): The latest time at which an activity can be started. LSij = LFij  Dij

30. 2 10 4 40 0 3 20 30 50 60 70 3 2 3 4 4 5 7 3 1 • Example: Activity Times 8 10 13 16 16 4 0 9 9 8 ES20-50 = EET20 = 2 EF20-50 = ES + D = 2 + 3 = 5 LF20-50 = LET50 = 13 LS20-50 = LF – D = 13 – 3 = 10

31. Network Analysis (Computation) Activity Floats • Total Float (TF) • Total float or path float is the amount of time that an activity’s completion may be delayed without extending project completion time. • Total float or path float is the amount of time that an activity’s completion may be delayed without affecting the earliest start of any activity on the network critical path.

32. Network Analysis (Computation) Activity Floats • Total Float (TF) • Total path float time for activity (i-j) is the total float associated with a path. • For arbitrary activity (ij), the total float can be written as: • Path Float =Total Float (TFij) • = LSij ESij • = LFij  EFij • = LETj – EETi  Dij

33. 40 2 10 4 0 3 20 30 50 60 70 3 3 2 4 4 5 7 3 1 • Example: Total Float Times 8 10 13 16 16 4 0 9 TF20-50 = LS20-50 - ES20-50 TF20-50 = 10 – 2 = 8 TF20-50 = LF20-50 - EF20-50 TF20-50 = 13 – 5 = 8 TF20-50 = LET50 – EET20 - D20-50 TF20-50 = 13 – 2 –3 = 8 9 8

34. Network Analysis (Computation) Activity Floats • Free Float (FF) • Free float or activity float is the amount of time that an activity’s completion time may be delayed without affecting the earliest start of succeeding activity. • Activity float is “owned” by an individual activity, whereas path or total float is shared by all activities along a slack path. • Total float always equals or exceeds free float (TF ≥ FF). • For arbitrary activity (ij), the free float can be written as: • Activity Float = Free Float (FFij) • = ESjk EFij • =EETj – EETi  Dij

35. 2 10 4 40 0 3 30 50 60 20 70 3 3 2 4 4 5 7 3 1 • Example: Free Float Times 8 10 13 16 16 4 0 9 9 8 FF20-50 = ES50-70 –EF20-50 FF20-50 = 8 – 5 = 3 FF20-50 = EET50 – EET20 - D20-50 FF20-50 = 8 – 2 –3 = 3

36. Network Analysis (Computation) Activity Floats • Interfering Float (ITF) • Interfering float is the difference between TF and FF. • If ITF of an activity is used, the start of some succeeding activities will be delayed beyond its ES. • In other words, if the activity uses its ITF, it “interferes” by this amount with the early times for the down path activity. • For arbitrary activity (ij), the Interfering float can be written as: • Interfering Float (ITFij) • = TFijFFij • = LETj EETj

37. 2 10 4 40 0 3 20 30 50 60 70 3 3 2 4 4 5 7 3 1 • Example: Interfering Float Times 8 10 13 16 16 4 0 9 9 ITF20-50 = TF20-50 - FF20-50 IFF20-50 = 8 – 3 = 5 ITF20-50 = LET50 – EET50 ITF20-50 = 13 – 8 = 5 8

38. Network Analysis (Computation) Activity Floats • Independent Float (IDF) • It is the amount of float which an activity will always possess no matter how early or late it or its predecessors and successors are. • The activity has this float “independent” of any slippage of predecessors and any allowable start time of successors. Assuming all predecessors end as late as possible and successors start as early as possible. • IDF is “owned” by one activity. • In all cases, independent float is always less than or equal to free float (IDF ≤ FF).

39. Network Analysis (Computation) Activity Floats • Independent Float (IDF) • For arbitrary activity (ij), the Independent Float can be written as: • Independent Float (IDFij) • = Max (0, EETj LETi – Dij) • = Max (0, Min (ESjk) - Max (LFli)  Dij)

40. 40 2 10 4 0 3 20 30 50 60 70 3 3 2 4 4 5 7 3 1 • Example: Independent Float Times 8 10 13 16 16 4 0 9 9 8 IDF20-50 = Max. (0, [EET50 – LET20 - D20-50]) IDF20-50 = Max. (0, [8 – 10 – 3]) = 0